Dummy variables

Applied Econometrics

Applied EconometricsSecond edition

Dimitrios Asteriou and Stephen G. Hall


DUMMY VARIABLES

1. The Nature of Qualitative Information2. The Use of Dummy Variables3. Special Cases of Dummy Variables4. Dummy Variables with Multiple Categories5. Tests for Structural Stability


Learning Objectives1. Understand the various forms of possible misspecification in the

CLRM.

2. Appreciate the importance and learn the consequences of omitting influential variables in the CLRM.

3. Distinguish among the wide range of functional forms and understand the meaning and interpretation of their coefficients.

4. Understand the importance of measurement errors in the data.

5. Perform misspecification tests using econometric software.

6. Understand the meaning of nested and non-nested models.

7. Be familiar with the concept of data mining and choose an appropriate econometric model.


The Nature of Qualitative InformationSometimes we can not obtain a set of numerical

values for all the variables we want to use in a model.

This is because some variables can not be quantified easily.

Examples:(a) Gender may play a role in determining salary levels

(b) Different ethnic groups may follow different consumption patterns

(c) Educational levels can affect earnings from employment


It is easier to have dummies for cross-sectional variables, but sometimes we do have for time series as well.

Examples(a) Changes in a political regime may affect production

(b) A war can have an impact on economic activities

(c) Certain days in a week or certain months in a year can have different effects in the fluctuation of stock prices

(d) Seasonal effects are often observed in demand of various products

The Nature of Qualitative Information


The Use of Dummy VariablesConsider the following cross-sectional model:

Yi=β1+β2X2i+ ui

The constant term in this equation measures the mean value of Yi when X2i is equal to zero.

This model assumes that the constant will be the same for all the observations in our data set.

But what if we have two different subgroups (male, female for example)?


The Use of Dummy VariablesThe question here is how to quantify the information

that comes from the difference in the two groups.

One solution is to create a dummy variable as follows:

1 for male

D =

0 for female

Note that the choice of which of the two different outcomes is to be assigned the value of 1 does not alter the results.


The Use of Dummy VariablesEntering this dummy in the equation we have the

following model:

Yi=β1+β2X2i+β3Di+ui

Now we have two cases

Di=0 Yi=β1+β2X2i+ β3(0) +ui

Yi=β1+β2X2i+ui

Di=1 Yi=β1+β2X2i+β3(1)+ui

Yi=(β1+β3) +β2X2i+ui


Intercept Dummy Variable

Y

X2

Red Points: Male

Grey Points: Female


Intercept Dummy Variable

β1+β3

X2

Y

β1


Slope Dummy VariableConsider the same case but now with the dummy

affecting the slopeYi=β1+β2X2i+β3DiX2i+ui

Now we have two cases

Di=0 Yi=β1+β2X2i+β3(0)iX2i+ui

Yi=β1+β2X2i+ui

Di=1 Yi=β1+β2X2i+β3(1)iX2i+ui

Yi=β1+(β2+β3)X2i+ui


Slope Dummy Variable

0

100000

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400000

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600000

700000

0 200 400 600 800 1000 1200 1400

Y

X2


The Combined EffectY

b1 +d

b1

Males

Femalesd

l


Dummies with Multiple CategoriesConsider the case of education:

D1= 1 primary; 0 otherwise

D2= 1 if secondary; 0 otherwise

D3= 1 if tertiary; 0 otherwise

D4 = 1 if BSc; 0 otherwise

D5 = 1 if MSc; 0 otherwise


The Plug in SolutionSo we estimate:

Y=β1+β2X2+ a1 D2+a2D3+a3D4+a4D5+u

Note that one dummy (in this case D1) is excluded from the model in order to avoid dummy variable trap.

Consider various cases,

i.e. D2=1, D3=D4=D5=0 etc.


Multiple Categories

-100000

0

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200000

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700000

0 200 400 600 800 1000 1200 1400

COST

N

Technical schools Vocational schools General schools Workers' schools


Using More than One DummyGENDER (male; female)

EDUC (primary, secondary, tertiary; BSc; MSc)

AGE (less than 30, 30 to 40; more than 40)

OCUP (unskilled, skilled, clerical, self-employed) etc

The interpretation (although it seems more complicated) is the same as before


Seasonal Dummy Variables

Depends on the frequency of the data

Quarterly – 4 dummies – DQ1, DQ2, DQ3, DQ4

Monthly – 12 dummies – one for each month

Daily – 5 dummies – Dmon, Dtue, Dwed etc.

Again we either exclude one and include a constant (always better) or if we use all we never include a constant (dummy variable trap).


The Chow Test for Structural Stability

Step 1: Estimate the basic regression equation.

Yi=β1+β2X2i+ui

for three different data sets (a)whole sample, n; (b)Period before the shock, n1;(c)Period after the shock, n2. Step 2: Obtain the SSR for each of the three subsets

and label them SSRN, SSR1 and SSR2 respectively.


The Chow Test for Structural Stability

Step 3: Calculate the F-statistic F

Step 4: If F-statistical bigger than F-critical F(k,n-2k) then reject the null that the parameters are stable for the whole data set.

)2/()(

/])[(

21

21

knRSSRSS

kRSSRSSSSRN


The Dummy Variable Test for Structural Stability

The Dummy Variable Test is much better because:• A single equation is used to provide a set of the

estimated coefficients for tow or more structures• Only one degree of freedom is lost for every

dummy used.• A larger sample is being used for the estimation• It provides us with information regarding the exact

nature of the parameter instability.

Dummy variables

Education

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